It is mentioned that Melkor is the most powerful of the Valar, so what stopped him making his own race? What held him back?
The Orcs don't count as he simply modified the elves.
Creation of living thinking beings is explicitly something that can only be done by Eru. Even when Aulë tried, in creating the Dwarves, he succeeded only in creating puppets, until Eru himself gave them life. There is no reason to think that Melkor would have been able to do this, even if he had tried.
As Daniel Roseman says, the ability to create what Tolkien calls "rational incarnate" life is solely given to Eru Ilúvatar, the capital-G God of Tolkien's Legendarium. No matter how hard he tried, Morgoth simply didn't have the power to grant souls to his creations. Tolkien draws an explicit comparison to Aulë and his dwarves in an essay printed in Morgoth's Ring, titled "Orcs":
Melkor was impotent to produce any living thing, but skilled in corruption of things that did not proceed from himself, if he could dominate them. But if he had indeed attempted to make creatures of his own in imitation or mockery of the Incarnates [Elves and Men], he would, like Aulë, only succeeded in producing puppets: his creatures would have acted only when the attention of his will was upon them, and they would have shown no reluctance to execute any command of his, even if it were to destroy themselves.
History of Middle-earth X Morgoth's Ring Part 5: "Myths Transformed" Chapter X "Orcs"
Which isn't to say he didn't give it the old college try; as Ainulindalë says, Melkor spent a great deal of "time"1 searching for the Flame Imperishable, which he believed would grant him this power:
To Melkor among the Ainur had been given the greatest gifts of power and knowledge, and he had a share in all the gifts of his brethren. He had gone often alone into the void places seeking the Imperishable Flame; for desire grew hot within him to bring into Being things of his own, and it seemed to him that Ilúvatar took no thought for the Void, and he was impatient of its emptiness. Yet he found not the Fire, for it is with Ilúvatar.
The Silmarillion I Ainulindalë
He's right, of course: the Flame Imperishable would grant him that power. Unfortunately, it's not something he can acquire. As Tolkien says, it is with Ilúvatar, and Ilúvatar alone.
1 Velociraptor air quotes here because time doesn't really make sense in the Timeless Halls
Melkor probably could have created his own race, if he were willing to use the same methods that the Valar did. But the Valar's methods were unacceptable to Melkor, and that put a self-imposed limit on what he could do.
The big thing to understand about Melkor is that his greatest wish is to act completely independently of Eru Iluvatar. He believes that in order to do this, he must do something that Eru does not allow him to do. He first tried to do this by modifying the Music, but he was frustrated when Eru simply incorporated those modifications. Now, what would satisfy him most would be to create free-willed beings without Eru allowing it.
Melkor was indeed the strongest of the Ainur. Technically he wasn't one of the Valar (which was more of an organization than a subrace of the Ainur), though he rivalled even them in power. Several of the Valar created living beings, and even Melkor is said to have created some monsters.
But there is one power that no Ainur has, not even Melkor: the Flame Imperishable, which bestows sentience on living things. None of the living things created by the Ainur were sentient until Eru "adopted" them, using the Flame to awaken minds in these creatures. Even the Dwarves and the Ents were not sentient until this time, as Eru points out.
This makes Eru a sort of gatekeeper: a being of sufficient power might create new plant and animal life, but to create an entirely new race of sentient beings requires not just his permission, but an explicit act on his part to grant them sentience. The Valar's method, therefore, effectively requires asking Eru's permission. Melkor does not have it, and more to the point, he does not want it. From Melkor's perspective, asking Eru for permission would defeat the whole purpose of the exercise: his creations would then be Eru's creatures, not his. So Melkor thinks, anyway.
Melkor believed that if he could find the Flame, he might be able to create sentient life without Eru's permission, but he never managed to find it. This isn't for lack of trying on his part. Most of his efforts were spent in a past so distant that time had no real meaning, but it is said that he was mighty and persistent in his search. But to no avail. Since he could not find the Flame, and would not borrow it from Eru, the creation of sentient life was closed to him.
Since that was not an option, Melkor set out to do what he considered the next best thing: he corrupted the existing creations. It did not satisfy him, because he was never able to ignore the fact that these were still Eru's creations, even if twisted by Melkor's will. He feared them for that reason, even as he used them. But they would have to do.
Because Tolkien probably believed that in real life creating life was utterly impossible and therefore could be done only by God Almighty who could work miracles.
Thus Tolkien made that the rule in his fictional universe of Arda, especially since it was supposed to be our world thousands of years ago.
In the earliest versions Melkor could create life, but as Tolkien made his legendarium more and more serious he made it more consistent with his Catholic theology and so Melkor could only modify life.
Of course once life already existed that was not really much of a limitation on Melkor since he now had the raw materials to modify in any way he saw fit.
Of course it seem pretty obvious that scientifically speaking in the real world creating life is not something terribly difficult or impossible and thus any theology which claims that God Almighty is the only person who can create life is certain to be proven wrong in just a few decades or centuries. So writers of future epic fantasy works need not imitate that feature of Tolkien's legendarium.